Determination of yield stress fluid behaviour from inclined plane test

The aim of this paper is to determine precisely under which conditions an inclined plane can be used as a rheometer, which could represent a practical and rapid technique for various types of industrial or natural viscoplastic coarse suspensions. We first examine its efficiency and relevancy for determining fluid yield stress in a straight way by measuring the deepest fluid layer able to stay on the inclined plane. We have made experiments with different materials (clay-water suspensions) whose yield stress ranged from 35 to 90 Pa, using 1 m long open rectangular channels with a slope ranging from 10 to 30° and a width ranging from 5 to 25 cm. Our procedure involved measuring the final fluid depth far from edges a long time after the end of the slow gravity-induced emptying of a dam placed upstream. The fluid yield stress was also estimated independently by fitting a Herschel-Bulkley model to simple shear rheometry data obtained within a relatively wide shear rate range. A good agreement between inclined rectangular channel tests and independent usual rheometrical tests is obtained even for aspect ratios (flow depth to channel width ratio) as large as 1 when one assumes that, when the fluid has stopped, the side and bottom wall shear stresses are equal to the fluid yield stress. These results prove the efficiency of the inclined plane test for determining yield stress when appropriate experimental precautions are taken for both tests. In addition we examine the possibility of determining the simple shear flow curve of a mud suspension from fluid depth, velocity and discharge measurements of different steady flows in a wide open channel (8 m long; 60 cm wide) equipped with a recirculating system. The results obtained from inclined plane tests are in good agreement with independent rheometrical data (with torsional geometries). However it is technically difficult to cover a wide shear rate range from the inclined plane technique since this requires a rather wide channel flow rate range.     

A cyclic anisotropic-plasticity model for metal matrix composites

Based on a six parameter general anisotropic yield surface proposed earlier by Voyiadjis and Thiagarajan (An Anisotropic Yield Surface Model for Directionally Reinforced Metal Matrix Composites, Int. J. Plasticity [1995]), a cyclic plasticity model to model the behavior of directionally reinforced metal matrix composite, has been proposed here. Apart from being able to model different initial yielding behavior along different stress directions, a number of features have been incorporated into the plasticity model. They include the usage of a proposed non-associative flow rule, kinematic hardening rule of Phillips type, a modified form of the bounding surface model for modelling the cyclic behavior, and the usage of a proposed form for evaluating the plastic modulus for anisotropic materials. Previous experimental data have been used for the evaluation of the yield surface parameters as well as those for the determination of the plastic modulus. The stress-strain results generated from the model have then been compared with those from the experiments. The behavior of the model under certain simulated cyclic loading situations has also been presented.     

MDYB-3有机玻璃在不同应变率下的一维屈服行为

对MDYB-3有机玻璃进行了多组不同应变率(10-3~3 000 s-1)下的压缩实验, 得到准静态下的屈服应力与动态下的峰值应力。沿其增强与面内2个方向进行准静态压缩实验, 以分析定向拉伸对屈服应力的影响, 修正了Ree-Eyring模型与Cooperative模型以描述定向有机玻璃的屈服行为。采用Johnson-Cook模型描述屈服后的黏塑性行为。结果表明Cooperative屈服模型比Ree-Eyring屈服模型更接近实验结果, 且能准确描述准静态屈服应力。动态压缩下的峰值应力为失效应力, 说明试样在1 500 s-1以上应变率下未达到屈服应力时已经发生破坏。Johnson-Cook模型对于单条曲线拟合良好, 但无法准确描述材料的应变率相关性。     

Cyclic ratchetting of 1070 steel under multiaxial stress states

Cyclic ratchetting behavior of 1070 steel is studied under proportional and nonproportional loading with specific emphasis on the ratchetting rate decay mechanisms for large numbers of loading cycles. Under proportional loading, where the principal stress directions are unchanged, the ratchetting evolves in the mean stress direction. Under nonproportional loading, however, the ratchetting direction is determined by the loading path and can be different from the mean stress direction. The ratchetting rate decreases with increasing loading cycles, displaying a power law relationship with the number of loading cycles. The experimental ratchetting results indicate that under cyclic loading the material exhibits a tendency toward complying with a linear hardening rule with concomitant hysteresis loop closure. Based on the fundamental framework of plasticity theory and detailed evaluation of the stress-strain behaviors, the ratchetting can be classified into two basic types; Type I, which is identifiable with proportional loading where the ratchetting is due to the different values of the plastic modulus function at the symmetric loading points with respect to the mean stress state, and Type II, which represents nonproportional loading where the ratchetting is driven by the noncoincidence of the plastic strain rate vector and the translation direction of the yield surface (backstress rate vector). The Armstrong-Frederick-based plasticity models modified by Chaboche et al. and Bower are ill-suited for describing the experimental results of both types of ratchetting. The Ohno-Wang model, which introduces a threshold concept, can account for the ratchetting rate decay of Type II ratchetting, providing results that agree with experimental observations. Modification may be needed for the Ohno-Wang model so that the model can better describe Type I ratchetting.     

Effect of source and obstacle strengths on yield stress: A discrete dislocation study

The combined effect of dislocation source strength τ_s, dislocation obstacle strength τ_obs, and obstacle spacing L_obs on the yield stress of single crystal metals is investigated analytically and numerically. A continuum theory of dislocation pileups emanating from a finite-strength source and impinging on asymmetric obstacles gives a closed-form expression for the yield stress. A 2d discrete dislocation model for a single-source/obstacle problem agrees well with the analytic model over a wide range of material parameters. Discrete dislocation simulations for a full tensile bar with statistically distributed sources and obstacles show that the distribution of obstacles plays a significant role in controlling the yield stress. Over a wide range of parameters, the simulations agree well with the analytic model using an effective obstacle spacing L_obs^* chosen to capture the strength-controlling statistically weaker pileup configurations. The analytic model can thus be used to guide the choice of source and obstacle parameters to obtain a desired yield stress. The model also shows how different combinations of internal source and obstacle parameters can generate the same macroscopic yield stress, and points to several internal length scales that could relate to size-dependent plasticity phenomena.     

岩土的一种强度准则及其变换应力法

基于岩土摩擦性,假设岩土破坏是由其物理空间内特征面上的应力比决定,提出了等效应力比的概念,即物理空间特征面上的剪应力合力与正应力合力的比值.在二维条件下,等效应力比可表示为σ-τ坐标系下与摩尔圆相切的直线扣除截距正切值;在三维条件下,假设在XYZ空间内存在一三维物理空间平面,此三维空间特征平面的等效应力比为影响材料强度特性的决定性因素,基于上述三维空间特征面建立了强度准则并称之为a准则.SMP准则以及广义Mises准则都是a准则的特例,当二维坐标中的截距为零时,则强度准则退化为SMP(spatially mobilized plane)强度准则,而当正切角为零时,则强度准则退化为广义Mises准则.而当截距与外切角均不为零时,则强度准则为介于上述两者之间的一种强度准则,在偏平面上为介于SMP曲边三角形与广义Mises圆形之间的曲边三角形.在子午面上,采用考虑岩土压剪耦合的屈服准则,破坏准则采用幂函数表达式.在偏平面上提出了基于a准则的形状函数,并采用真三维应力状态表示的破坏强度准则表示在三轴压缩路径下以p,q二维应力变量表达的准则公式,推导得到了基于a准则的变换应力公式,可简单地将一般以p,q为基本变量的二维模型转变为三维应力模型.通过强度以及多种应力路径的测试对比,验证了a准则及基于该准则的变换应力公式的合理性.     

Anisotropic work hardening of steel sheets under plane stress

This work is a follow-up of the previous report by Kim and Yin [Kim, K.H., Yin, J.J., 1997. Evolution of anisotropy under plane stress. J. Mech. Phys. Solids 45, 841–851] regarding the anisotropic work hardening of cold rolled steel sheets. Tensile prestrain has been applied at angles to the rolling direction and then tensile uniaxial yield stress and R-value distributions are measured. As reported earlier, the orientations of local maxima and minima in the yield stress are altered when the prestrain axis is not in the rolling direction. This led Kim and Yin [Kim and Yin (1997)] to suggest that the orientations of orthotropy axes are altered by the tensile prestrain at angles to the rolling direction. However, R-value distribution is found to be hardly affected by the prestrain. The unchanging R-value distribution shows that the material remembers the rolling direction even after the prestrain. An attempt is made to approximate the observed yield and flow behavior based upon isotropic-kinematic hardening with the quadratic yield function (Hill, 1948). The degree of approximation raises the issues of yield point definition, flexibility of yield function, non-associated flow rules, distortional hardening and others.     

Long-term strength of metals in complex stress state (a survey)

An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given. In Sections 2 and 3, the results of plane stress tests (with opposite and equal signs of the nonzero principal stresses, respectively) are analyzed. In Section 4, the results of inhomogeneous stress tests (thick-walled tubes under the action of internal pressures and tensile forces) are considered. All known experimental data (35 test series) are analyzed by a criterion approach. An equivalent stress σ _e is introduced as a characteristic of the stress state. Attention is mainly paid to the dependence of σ _e on the principal stresses. Statistical methods are used to obtain an expression for σ _e, which can be used to study various types of the complex stress state. It is shown that for the long-term strength criterion one can use the power or power-fractional dependence of the time to rupture on the equivalent stress. The methods proposed to describe the test results give a good correspondence between the experimental and theoretical values of the time to rupture. In Section 5, the possibilities of complicating the expressions for σ _e by using additional material constants are considered.     

π平面上原状土的空心扭剪试验

为了通过空心扭剪试验获得原状土在π 平面上的屈服特性,在分析空心扭剪试验仪加载过程和加载特点的基础上,研究了空心圆柱试样可实现的应力状态,并设计了相应的加载路径．与重塑试样不同,原状土样的初始应力状态位于K0 固结线上而不是等倾线上,因此,其加载路径应从原点开始沿K0 固结线行至原始应力状态,然后再在π 平面上进行以初始应力为起点的等p 试验．在考虑原状土的初始应力状态和各项异性的基础上,针对具有不同主应力方向角的平行试样,给出了等p 条件下保持主应力方向角不变的加载路径实现方法,采用该方法可得到任意平均主应力时π 平面上六分之一范围内的屈服曲线,该范围对应于大主应力方向角从-45o~45o．本文设计的加载方案可完成真三轴试验的部分功能,但经济成本相对较低,操作方法简单易行．     

On the relationship between critical tensile stress and fracture toughness in mild steel

An analysis is presented which relates the critical value of tensile stress (σ_f) for unstable cleavage fracture to the fracture toughness (K_Ic) for a high-nitrogen mild steel under plane strain conditions. The correlation is based on (i) the model for cleavage cracking developed by E. Smith and (ii) accurate plastic-elastic solutions for the stress distributions ahead of a sharp crack derived by J. R. Rice and co-workers. Unstable fracture is found to be consistent with the attainment of a stress intensification close to the tip such that the maximum principal stress σ_yy exceeds σ_f over a characteristic distance, determined as twice the grain size. The model is seen to predict the experimentally determined variation of K_Ic with temperature over the range -150 to -75°C from a knowledge of the yield stress and hardening properties. It is further shown that the onset of fibrous fracture ahead of the tip can be deduced from the position of the maximum achievable stress intensification. The relationship between the model for fracture ahead of a sharp crack, and that ahead of a rounded notch, is discussed in detail.     

An orthotropic yield criterion in a 3-D general stress state

An anisotropic yield criterion with a general representation was suggested. The yield criterion was derived from the use of the invariants of the stress tensor, similar in constructing an isotropic yield criterion, but which contains a “three-yield-system hypothesis” specifying the state of anisotropy. When applied to rolled sheet metals, such as high strength steels and aluminum alloys, the criterion can be treated in an analytical form to facilitate analyses of engineering problems under a general triaxial stress state. For this specified form, anisotropic properties of the predicted yield surface were characterized by seven experimental results obtained from three standard uniaxial-tension tests and one equibiaxial-tension test. When the applied material becomes isotropic it is transformed back to the form of the von-Mises’s criterion. Since the convexity of the yield criterion was proven in its general type, the characterized criterion is valid as a plastic potential in the implementation of finite element programs. It was shown, in full agreement with experimental data, that the accuracy of predicted yield surface was similar to that of predicted by the polycrystal model. Considering the equibiaxial-tension data, in general, may be not available from material supplies, a formulated relation covered variables of the equibiaxial tension and uniaxial tension was proposed. The relation can be used to calculate the equibiaxial-tension yield stress from the experimental data in uniaxial tensions. Several calculated results showed very close to the experimental results.     

Modelling inelastic behaviour of orthotropic metals in a unique alignment of deviatoric plane within the stress space

A finite strain constitutive model to predict the deformation behaviour of orthotropic metals is developed in this paper. The important features of this constitutive model are the multiplicative decomposition of the deformation gradient and a new Mandel stress tensor combined with the new stress tensor decomposition generalized into deviatoric and spherical parts. The elastic free energy function and the yield function are defined within an invariant theory by means of the structural tensors. The Hill’s yield criterion is adopted to characterize plastic orthotropy, and the thermally micromechanical-based model, Mechanical Threshold Model (MTS) is used as a referential curve to control the yield surface expansion using an isotropic plastic hardening assumption. The model complexity is further extended by coupling the formulation with the shock equation of state (EOS). The proposed formulation is integrated in the isoclinic configuration and allows for a unique treatment for elastic and plastic anisotropy. The effects of elastic anisotropy are taken into account through the stress tensor decomposition and plastic anisotropy through yield surface defined in the generalized deviatoric plane perpendicular to the generalized pressure. The proposed formulation of this work is implemented into the Lawrence Livermore National Laboratory-DYNA3D code by the modification of several subroutines in the code. The capability of the new constitutive model to capture strain rate and temperature sensitivity is then validated. The final part of this process is a comparison of the results generated by the proposed constitutive model against the available experimental data from both the Plate Impact test and Taylor Cylinder Impact test. A good agreement between experimental and simulation is obtained in each test.     

NONLINEAR UNIFIED STRENGTH MODEL OF GEOMATERIALS

将材料的破坏归结为剪切破坏,每种材料对应于特定的剪切滑动面,抗剪强度为滑动面上正应力的函数,基于不同材料的强度特性将一系列的剪切滑动面统一起来,建立了岩土材料的非线性统一强度模型.非线性统一强度模型的滑动面为β应力空间内的等倾面,在β应力空间内的强度面为圆锥面;在普通应力空间内的强度面为一系列连续光滑、外凸的锥面,在偏平面上强度曲线涵盖了从下限Matsuoka-Nakai曲线到上限Drucker-Prager圆之间的所有区域,子午面上强度线为直线.非线性统一强度模型只有3个材料参数,参数都具有明确的物理意义,通过与国内外学者已取得的岩土类材料真三轴强度试验结果的比较,表明模型可适用于多种类型的材料,并合理描述其非线性强度特性.     

一种适用于岩土的扩展强度及屈服准则

土壤材料是一种典型的摩擦型材料,然而天然岩石却具有一定的凝聚力,而金属材料则完全是凝聚型材料. 在分析三种典型的材料强度准则表达式基础上,即SMP,Lade-Duncan以及广义Von-Mises准则,通过利用应力张量的不变量表达形式,提出了一种扩展准则即VML准则,该准则能够分别退化为上述3种典型准则. 在偏平面上,新准则能够描述从曲边三角形到圆形在内的多种开口形态;在子午面上,采用幂函数作为破坏准则公式,能够描述静水压力对于强度特性影响的非线性性质. 而对于土壤的屈服性质,岩土材料具有典型的压剪耦合特性,因此,为了描述剪切与等方向压缩两种路径下的体积耦合现象,采用水滴型屈服面作为屈服准则. 对于偏平面上的截面形状,讨论了给定球应力下偏应力强度值的分布形式及特点,讨论了应力罗德角对于偏平面上强度曲线的凹凸性的影响. 最后,通过多种材料的破坏与屈服试验成果,用所提新准则进行了验证. 通过强度以及屈服特性测试对比,验证了所提VML准则的合理性.      

Physical invariants for nonlinear orthotropic solids

Seven invariants, with immediate physical interpretation, are proposed for the strain energy function of nonlinear orthotropic elastic solids. Three of the seven invariants are the principal stretch ratios and the other four are squares of the dot product between the two preferred directions and two principal directions of the right stretch tensor. A strain energy function, expressed in terms of these invariants, has a symmetrical property almost similar to that of an isotropic elastic solid written in terms of principal stretches. Ground state and stress–strain relations are given. Using principal axes techniques, the formulation is applied, with mathematical simplicity, to several types of deformations. In simple shear, a necessary and sufficient condition is given for Poynting relation and two novel deformation-dependent universal relations are formulated. Using series expansions and the symmetrical property, the proposed general strain energy function is refined to a particular general form. A type of strain energy function, where the ground state constants are written explicitly, is proposed. Some advantages of this type of function are indicated. An experimental advantage is demonstrated by showing a simple triaxial test can vary a single invariant while keeping the remaining invariants fixed.     

Evaluation of identification methods for YLD2004-18p

Four calibration methods have been evaluated for the linear transformation-based anisotropic yield function YLD2004-18p (Barlat, F., Aretz, H., Yoon, J.W., Karabin, M.E., Brem, J.C., Dick, R.E., 2005. Linear transformation-based anisotropic yield functions. Int. J. Plasticity 21, 1009–1039) and the aluminium alloy AA5083-H116. The different parameter identifications are based on least squares fits to combinations of uniaxial tensile tests in seven directions with respect to the rolling direction, compression (upsetting) tests in the normal direction and stress states found using the full-constraint (FC) Taylor model for 690 evenly distributed strain paths. An elastic–plastic constitutive model based on YLD2004-18p has been implemented in a non-linear finite element code and used in finite element simulations of plane-strain tension tests, shear tests and upsetting tests. The experimental results as well as the Taylor model predictions can be satisfactorily reproduced by the considered yield function. However, the lacking ability of the Taylor model to quantitatively reproduce the experiments calls for more advanced crystal plasticity models.     

A yield function for single crystals containing voids

A yield function for single crystals containing voids has been developed based on a variational approach. This first yield function is phenomenologically extended by modifying the dependence on the mean stress and introducing three adjustable parameters. Unit cell finite element calculations are performed for various stress triaxiality ratios, main loading directions and porosity levels in the case of a perfectly plastic FCC single crystal. The three model parameters are adjusted on the unit cell calculations so that a very good agreement between simulation results and the proposed model is obtained.